A078511 Numbers k such that sopfr(k)=tau(k).

2, 60, 72, 168, 270, 450, 560, 990, 1056, 1188, 1470, 2496, 3200, 3402, 3520, 3672, 4788, 5700, 8320, 9856, 9936, 10164, 10395, 11000, 11160, 12180, 12740, 13056, 13720, 14616, 16524, 17400, 17940, 18522, 19380, 20000, 20475, 21252, 21528

Offset: 1

Author

Benoit Cloitre, Jan 11 2003

Keywords

• nonn

Comments

It appears Sum_{n=1..m} a(n) =~ c*sqrt(m)*(log(m) - log(log(m))^2), at c ~ 0.038, asymptotically, after examining m up to 10,000,000, with data intervals of 10,000. - Richard R. Forberg, Feb 10 2015

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001414.

Programs

Mathematica

s = {}; Do[If[DivisorSigma[0, n] == Total[Times @@@ FactorInteger[n]], AppendTo[s, n]], {n, 2, 22000}]; s (* Amiram Eldar, Jun 22 2019 *)

PARI

isok(n) = {my(f = factor(n)); sum(i=1, #f~, f[i,1]*f[i,2]) == numdiv(n);} \\ Michel Marcus, Feb 11 2015

Formula

A001414(a(n)) = A000005(a(n)).